A vertex-allocation theorem for resources in queuing networks

Satish K. Tripathi · C. Murray Woodside

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Advanced Queuing Theory Analysis Distributed and Parallel Computing Systems Optimization and Search Problems

Abstract

A product-form queuing network with multiple open and closed chains is considered. Some of the closed chains, which have a single customer each, require allocation of resources in the network so as to maximize a weighted throughput performance criterion. Chains with more than one customer can be decomposed into many chains of one customer each. It is proved that an optimal allocation of resources lies on a vertex (extreme points) of the set of feasible allocations. This considerably reduces the search space for an optimal allocation. Applications of this result in distributed computing are discussed.

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1975Open, Closed, and Mixed Networks of Queues with Different Classes of Customers 1985Optimal static load balancing in distributed computer systems 1980Queueing network models of multiprogramming 1983Optimal routing in closed queuing networks

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2011Optimal Routing in Closed Queueing Networks with State Dependent Queues

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